A buoy is floating in the sea and can be seen from the top of a vertical cliff. A boat is travelling from the base of the cliff directly towards the buoy. The top of the cliff is 142 m above sea level. The angle of depression

from the top of the cliff to the buoy is 40 degrees.

169.23m

Step-by-step explanation:.

Let's calculate the base of the cliff. Using SOH CAH TOA identity

Height (opposite) = 142n

Angle of depression = 40°

Required

Base of the cliff

Tan theta = opposite/adjacent

Tan 40 = 142/x

x = 142/tan40

x = 142/0.8391

x = 169.23m

Hence the base of the cliff is 169.23m long

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.